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NATIONAL BUREAU OF STANDARDS -1963
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65-32
To be submitted for publication
Phys. Rev. Letters.
in
MAY“5 1986
ON THE TEMPERATURE DEPENDENCE OF THE GJNZBURG-LANDAU PARAMETER*
S. T. Sekula and R. H. Kernohan
Solid State Division, Oak Ridge National Laboratory
Oak Ridge, Tennessee
MASTER
CFSTI PRICES
H.C. $ 10B; MN 56
The first extension of the Ginzburg-Landau-Abrikosov-Gori kov theory
appreciably below the superconducting transition temperature was given by
Gori kovl!) for type II superconductors of large mean free path of --> 0).
Maki") discussed the complete temperature dependence of Hc2, the upper
critical field, for alloys of small mean free path. Helfand and Werthamer,
in more recent work, have solved the general problem of the temperature de-
pendence of Hc2 from the clean to dirty limit and their results are in
general agreement with the earlier work.
On the other hand, while some experimental data were found to agree with
these calculations, (4) other workers (5) report a temperature dependence
greater than that expected from the theories. We have studied a Pb-27 at. %
Ti alloy and also found the temperature dependence of the Ginzburg-Landau
parameter to be larger than predicted. (6) Rosenblum and Cardona have found
a variation in the strength of the temperature dependence of the Ginzburg-
Landau parameter in several alloys which suggests a greater temperature de-
pendence for strong coupling superconductors.
It is the purpose of this letter to point out that a more detailed
examination of the present theory in terms of the different behavior of weak
and strong coupling superconductors can resolve a large portion of the dis-

crepancy between theory and experiment.
ill i ti til 1:1.130 1.1:
RELEASED FOR ANNOUNCEMENT
.: IN NUCLEAR SCIENCE ABSTRACTS
*Research sponsored by the U. S. Atomic Energy Commission under contract
Tor
with the Union Carbide Corporation.
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will the Comatolog, or his employment mild such contractor.
en la manera month and release
to be seen F PALESTINE
Tops PRACUDAS FILETIN RECEIVING
SECTION.
In Fig. 1, we reproduce with the kind permission of E. Helfand and N. R.
Werthamer, a plot of their calculations in a slightly different form as given
in their recent publication. Here h* = - Hc2(t) is plotted against the
OH.2
atti
reduced temperature for materials of extreme degrees of purity. The curves
Labeled 2 = 0 and 1 = o correspond to materials in the clean and dirty limit
respectively. On writing Hc2(t) = V218164) alt) H.(t), where H.2(t) is the
upper critical field, *(1) is the Ginzburg-Landau parameter at t = 1, alt)
the temperature dependence of the parameter, and Hc(t) the thermodynamic
critical field, one can write
*
-a(t) H.(t) --X(t,0) Hd (t).
7 . TOT
XT1,77 d. (t)
(2)
at
de
tal
tel
It is then clear that Fig. 1 of reference 3 implicitly contains certain
features of a thermodynamic model which is in fact the BCS weak coupling
model. While the difference in H.(t) is not large for strong and weak
coupling superconductors (given a value of H. and Tc), the derivation in eq.
(1) is quite sensitive to the degree of coupling and is approximately 20% larger
for strong coupling materials as compared to the BCS model. Thus the strength
of the temperature dependence of the Ginzburg-Landau parameter will vary as .
the degree of coupling.
Experimental data for a Pb 27 at. % Tl alloy and a Pb 7.4 at. % Tl alloy
are shown in Fig. I for purposes of comparison. The normal state resistivities
for these alloys were found to be 4.1 wa cm and 14.9 na cm. The experimental
points should lie between the calculated curves for the two extreme. limite,
and the general agreement is seen to be good. However, the temperature
-3-
dependence of the alloy with larger Tl concentration appears to be greater
than that of the sample with the larger electrical mean free path, and the
reasons for this discrepancy are not yet understood.
In Fig. 2 is silown a plot to obtained from magnetization data
using a ballistic techr.ique. (6) The values obtained are considerably larger
than those predicted by the theory using the BCS model and are attributed to
the strong coupling character of these alloys.
We would like to thank E. Helfand for valuable discussions.
Us
.
•--
REFERENCES
1. L. P. Gor' kov, Zh Eksperim. i Teor. Fiz. 37, 833 (1959).
[Translation: Soviet Phys. - JETP 10, 593 (1960).
2. K. Maki, Physics 1, 21 (1964).
3. E. Helfand and N. R. Werthamer, Phys. Rev. Letters 13, 686 (1964). -
4. T. Kinsel, E. A. Lynton and B. Serin, Rev. Mod. Phys.-36, part 1, 105
(1964).
5. A. Paskin, M. Strongin, P. P. Craig and D. G. Schweitzer, Phys. Rev.
A137, 1816 (1965).
6. S. T. Sekula and R. H. Kernohan (submitted for publication in J. Appl. Phys.).
7. B. Rosenblum and M. Cardona, Phys. Letters 13, 33 (1964).
FIGURE CAPTIONS
Fig. 1
The reduced parameter h* as a function of reduced temperature.
The solid curves are due to Helfand and Werthamer. Experimental
points for Pb 27% TI and Pb 7.4% TI are also shown.
Fig. 2
The reduced Ginzburg-Landau parameter
as a function of
the reduced temperature for Pb 27% TI and Pb 7.4% Tl.
ORNL-DWG 65-3740

o
8
0.6
0.5
0.
.
3*
-
**= -(dHc2/01),
ALLOY
ALLOY
o Pb-27 % TI
+ • Pb-7.4% TI
for me)
8230 oe
3270 oe
0.4L
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
ORNL-DWG 65–3741
i
1.3
.
:
.
o Pb-27 % TI « (1) = 3.79
• Pb-7.5% TI « (1) = 1.23
:
1.04
0

0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Yuri
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5 / 12 / 66
DATE FILMED
END
matin mamizhamur








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